Chapter 27 Basic Electric Circuits
Scientific work on electric circuits began around 1800 when Volta developed a reliable battery. When was electricity made available to the general population in the United States?
Electric Current
Electric Current, I, measures of the movement of charge. In a wire only the electrons move. If 1 Coulomb of charge moves through a cross section of a wire in one second then we can say that the current is 1 Ampere (1 Amp).
*Calculate the number of electrons that move through the cross section of the wire every second if the current is 1 Amp.
You should take a look at the circuit breaker box in your home sometime. Note the numbers on the circuit breakers ( 15, 20, 30). Those numbers represent the maximum current that will be allowed to exist in the portion of wiring in the house that connects to that circuit breaker. In the past fuses were used that melted when the current exceeded the preset value. Circuit breakers contain a switch that opens when the current value becomes too high. This switch can be reset but should only be reset after someone knows why the current became too high.
Can you measure the length of time between the instant a light switch is turned to the on position and the instant when the light starts emitting visible light? Why is this time so short? Does this help you estimate the speed of electrons in a wire?
When you put the light switch to the on position the wire experiences a potential difference from one end of the wire to the other end. This establishes an electric field in the wire. We can say that the conduction electrons are accelerated by this electric field. In a solid that has a current, the electrons are colliding with atoms in the wire. The electrons are accelerated but in a short distance a collision occurs with an atom in the wire and the electron rebounds in some random direction. A typical value for the net velocity of electrons in a wire is 5 x 10-5 m/s. This is called the drift velocity.
Calculate the length of time required for one electron to travel from the battery in a flashlight to the light bulb.
Why does a light bulb in a flashlight or in a light fixture in a room start emitting light so soon?
page 3 Positive and Negative Currents
For most situations a current of positive charges in one direction produces the same electrical effects as a current of negative charges in the opposite direction. Remind me to discuss this after we discuss magnetic forces on moving charges.
page 5 A Convention
Rewrite the sentence in the first paragraph: "It also leads to the unfortunate intuitive picture that an atom that has lost some electrons ends up with a positive charge."
Conventional Current
The work of Benjamin Franklin led to a description of current as the motion of positive charge. We will label circuits as if positive charge is moving in the wire. This is not correct but it is the traditional way circuits are labeled.
page 6 Current and Voltage
A higher voltage (potential difference from one end of a wire to the other end) is associated with a larger E field, a larger force on the electrons, and a larger current. In the 1800’s the voltage was called the "Electromotive Force", EMF. Voltage is not force but in the 1800’s the analogy was that greater voltage led to greater force on the charges. In some other physics books you may encounter the term, EMF.
Resistors
Resistance, R, measures the opposition to the movement of charge. The material in a resistor is less conductive than material in a wire and the electrons in the current have a more difficult time making progress through the circuit. The unit of resistance is the Ohm, W . If the resistance value for a wire is high the current will be small (as long as the voltage is a constant value).
A resistor that has a current I in the resistor will have a potential difference from one end of the resistor to the other end. The potential difference V = I R . This is known as Ohm’s Law. Materials that have a constant resistance as the V changes are said to "obey" Ohm’s Law. They are called "ohmic" materials. Semiconductors are non-ohmic. For common operation, wires and carbon resistors are ohmic. If the temperature of a material changes significantly the material will be non-ohmic.
Calculate the voltage across a 120 ohm resistor that is carrying a current of 25 milliamps.
Common resistors are made from carbon. The carbon is compacted and constructed with a certain cross section area and certain length that produces a certain value for its resistance. Values of less than 1 ohm to millions of ohms are easy to produce. Resistors can also be made from wires of a given diameter and length, and from semiconductor materials.
page 8 A Simple Circuit
The text shows the conventional symbols used for drawing circuits. These drawings are sometimes called schematic diagrams. We will use the convention that the negative pole of the battery is at 0 volts. We will assume that wires are ideal, that is, the wires have 0 resistance.
Calculate the resistance required to produce a current of 24 milliamps in a circuit where the battery has a voltage of 6 volts.
page 9 The Short Circuit
* What happens to the value of current when the value of R decreases?
If R approaches zero in a real circuit you would have to account for the resistance in the wire. The current would not become infinite. But, a dangerous level of current may exist, the wire may get hot, the battery could become dead, etc. Do not create a short circuit during our lab activities.
Power
The power in a circuit element is calculated using
Power (watts) = I (current in amps) V(potential difference in volts) P = IV
Calculate the power in a resistor that has a current of 24 milliamps and a voltage of 6 volts.
IF a resistor obeys Ohm’s Law then the power can be calculated with P = I2R
Repeat the calculation at the bottom of page 2 with this new formula for power.
page 10 Kirchoff’s Laws
PHY162 will cover this material.
page 11 Series Resistors
Resistors connected in "series" have the same current value even when the R’s are different values.
The net resistance, RS , is the sum of the individual resistance values.
RS = R1 + R2 + R3 + ...
Will the potential difference across each resistor be the same value?
What is true concerning the sum of the potential differences and the battery voltage?
We will work an example on a "voltage divider."
page 12 Parallel Resistors
Resistors connected in parallel have the same potential difference across each resistor even though the R’s are different values.
The net resistance, RP , is calculated as shown below.
1 1 1 1
----- = ----- + ----- + ----- …
RP R1 R2 R3
Why is the net parallel resistance smaller than any of the individual resistor values?
Will each resistor have the same current value?
Homes can be thought as having a certain electrical resistance. As homes are connected to the commercial electrical power grid, are they being connected in series or parallel?
A certain string of Christmas tree lights goes dark when one bulb fails. Are the lights connected in series or parallel?
An ohmmeter is a device that can be used to measure the resistance value. Modern ohmmeters use semiconductors to determine the resistance value. You should not use an ohmmeter on a resistor that is already wired into a circuit.
page 24 Capacitance and Capacitors
We encountered capacitors in a previous chapter. This chapter expands on their use in circuits and how the capacitance value can be modified other than by the area and plate separation.
A capacitor stores charge and thus can be used as a storage medium for electrical energy.
The amount of charge on a capacitor is determined by the capacitance value and the potential difference across the capacitor.
Q = C V
page 16 This is a review of the previous material on capacitors.
In a previous class we calculate the length of sides on a parallel plate capacitor that had a capacitance value of 1 Farad. When the distance between the parallel plates is reduced, what happens to the required area to make a 1 Farad capacitor? Calculate the length for the case of d = 1 x 10-9 meter, C = 1 Farad.
page 18 Energy Storage in Capacitors
Work is required to move charge onto the plates of a capacitor. This effectively stores energy (although energy is not a tangible substance) in the capacitor. A charged capacitor can do work (e.g. make a light bulb emit light).
The energy stored in a capacitor is = C V2 / 2 .
It is useful to define an energy density. It turns out to be ε0 E2 /2, where E is the electric field between the plates of the capacitor.
page 20 Capacitors as Circuit Elements
Capacitors can be placed in circuits in either series or parallel arrangements. If the positive plates of the capacitors are connected they are in parallel.
parallel capacitors CP = C1 + C2 + C3 + ...
The potential difference across each capacitor will be different (if the C’s are different).
Series The charge on the individual capacitors connected in series will be the same even though the C’s are different.
1 1 1 1
----- = ----- + ----- + -----
CS C1 C2 C3
page 22 The RC Circuit
Now we will investigate the combination of resistors and capacitors in a circuit.
Imagine that a resistor and capacitor are connected. The capacitor had a charge Q before the connection was made.
*Is there a potential difference across the plates of the capacitor before the connection is made?
Describe the amount of charge on the capacitor as time advances.
The formula that describes the potential difference across the capacitor is
Discharge V = Voe -t/RC
Imagine that a resistor, capacitor and battery are connected in series.
How will a resistor in series with a capacitor and battery affect the rate of charging of the capacitor?
Let the potential difference of the battery be given by the symbol EMF.
Charging VC = EMF(1 - e -t/RC )
The factor RC is called the time constant of the circuit.
Calculate V, in symbols, for the RC (discharge) circuit for the case of t = RC.
Skip pages 28 – 32.
Miscellaneous Topics
Why is the value of the internal resistance of a battery important?
Vterminal = EMF - Ir
Why does a battery loose its ability to deliver significant current to a circuit?
What is an advantage of connecting batteries in series?
What is an advantage of connecting batteries in parallel?
Know how to construct a voltmeter or ammeter from a galvanometer
Why do meters change the voltage or current values in a circuit?
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